Novel fractional modeling based on CATTANEO heat flux for enhancing thermal performance of u-tube parabolic trough collectors

This paper presents a new approach for modeling U-type parabolic trough collectors (PTCs). The model incorporates a concept called "time-fractional single-phase-lag" and accounts for thermal wave effects within the collector. Researchers first optimized the model using experimental data from Kafrelsheikh, Egypt, to achieve the most accurate predictions. Optimum solution obtained was for the case of fractional Fourier model, where 𝛽 = 0.8, and 𝜏 = 0, at which calculated average water outlet temperature was 50.872 °𝐶 compared with an average value of 50.885 °𝐶 obtained from experimental results. The most significant performance improvements were achieved by coating the absorber tube with black paint containing nanoparticles. Here, the best results were obtained with a 5% mass concentration of carbon nanotubes (CNTs) in the paint. This configuration led to a substantial increase in the average water temperature difference between the outlet and inlet (21.7 °𝐶) and a significant improvement in overall thermal efficiency (33.67%).